Calculus question and answers for January 12, 2024
- Q Using separation of variables technique solve the following differential equation with initial condition 1 and y 3 5 The solution is dy yx 5x dz O A In y 5...
- Q Suppose you want to find an equation for a curve whose slope at any point x y is x 6y2 You d need to solve the differential equation x 6y...
- Q yy ex 0 and y 4 when x 0 which means that O A In x 4 6 OB 2 4x 3 O c y 2x x OD y x...
- Q Which of the following differential equations with initial condition yields a solution curve that exhibits modified exponential growth such that y goes to negative infinity as t goes to positive...
- Q Solve the following differential equation with initial conditions y e 2t 10e t y 0 1 y 0 0 The solution is 5 4t O A y e e 3t...
- Q he acceleration of a particle moving along the x axis at time tis given by a t 6t 2 If the velocity is 25 when t 3 and the position...
- Q Graph I Graph II Graph III Click here for long description Graph IV
- Q 5x 1 An equation of the line tangent to the graph of y 3 1 at the point where x 1 is A 9x 7y 53 B 2x 3y 13...
- Q The family of curves represented on this graph would appear to be consistent with which of the following differential equations A d B D da Y Te tan x y...
- Q Let f be the function defined by f x X Which of the following statements is true OA fis discontinuous at x 0 B fis an odd function O c...
- Q Consider the position function s t 4 9t 25t 25 Complete the following table with the appropriate average velocities and then make a conjecture about the value of the instantaneous...
- Q For the following function make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at the indicated point f x 11...
- Q The maximum value of f x e x is OA 1 OB 1 OC 2 OD In 2 OE O
- Q For the position function s t instantaneous velocity at t 0 Time Interval Average Velocity 0 1 Complete the following table Time Interval 18 t 1 0 1 complete the...
- Q The graph of y g x is shown below At which point is g g OA A B B O C C D D OE E LA B C D...
- Q Which of the following differential equations is are not separable 1 t yt 1 dt II d y dx 3xy III dy y yx da O A I only O...
- Q 13 16 Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a 13 f x 3x x 2...
- Q Factor completely Then solve p w 3w 6w 24w
- Q 9 Discontinuities at 0 and 3 but continuous from the right at 0 and from the left at 3
- Q A rock is dropped off the edge of a cliff and its distance s in feet from the top of the cliff after t seconds is s t 16t Assume...
- Q a Graph the function f x x 4x 3 b Identify the point a f a at which the function has a tangent line with zero slope c Confirm your...
- Q Consider the position function s t 4 9t 291 17 Complete the following table with the appropriate average velocities and then make a conjecture about the value of the instantaneous...
- Q If the graph of y A 5 B 1 asymptote x 3 then a c C 5 D 1 E 0 ax b x c has a horizontal asymptote y...
- Q If x 2xy y 2 at the point 1 1 dy is da A 0 1 OB B 2 O C 12 2 OD nonexistent OE
- Q The differential equation dy dx O A y Cekt OB y C x 4 O C y Ce x O D y e C E x y C af has...
- Q Which of the following is not a differential equation A y 0 dx OB 4 y 2x dy c x x dx 4 y Y O D t 1 2...
- Q The change in the momentum of an object Ap is given by the force F acting on the object multiplied by the time interval that the force was acting Ap...
- Q A separable differential equation is a first order differential equation that can be algebraically manipulated to look like A Both f y dy g x dx and f x dx...
- Q If y5 3x y 5x4 49 then at the point 1 2 is dy dx O A 11 23 OB 11 23 O C 1 O D OE O 10...
- Q A solid has as its base the circular region in the xy plane bounded by the graph of x y2 4 Find the volume of the solid if every cross...
- Q If y5 3x y 5x4 49 then dy at the point 1 2 is dx O A OB 11 23 O C 1 11 O D OE O D 100...
- Q limx 9x x 7x4 x 12x A 9 OB 7 O C C 72 12 OD 7 O E Does not exist
- Q Suppose a certain country s population has constant relative birth and death rates of 97 births per thousand people per year and 47 deaths per thousand people per year respectively...
- Q The temperature over a given period is Estimate the average temperature from 0 t 8 using the left endpoints of four equal subintervals Time hours 0 1 2 3 4...
- Q OA ye dy xdx O B ydy xe d C None of these The equation is not separable OD ydy xe dx E udy re 2 dr
- Q The area of the region in the first quadrant between the graph of y k 4x x 0 and x axis where k 0 is OA KT B 2 k...
- Q dx ves the slope at any point on the graph of the f 2 8 A Write the equation of the tangent line to f x at point 2 8...
- Q Which of the following graphs is consistent with the differential equation dy dz 2 O A B C D E Vi
- Q is increasing at a rate directly proportional to 3500 C t Also C 0 1000 and C 5 2000 A Find C t as a function of t only B...
- Q X 0 9 1 0 1 1 Given h x 5 3 5 0 4 7 evaluated at x 5 O A 3 OB 3 O C 1 O D...
- Q Consider the following graph of y f x 40T 2 20 0 20 40 60 2 4 O A I only OB II only O C III only OD II...
- Q Let f be a polynomial function with degree greater than 2 If a b and f a f b 1 which of the following must be true for at least...
- Q The average value of the function g x 3cos on the closed interval T is OA 7 593 OB 4 347 O C 1 325 OD 18 068 OE 30...
- Q Which of the following is a separable first order differential equation O A y 2 In xy x y OB d x Y O c dy da xy x y...
- Q If f 2 2 5 and f 2 2 5 then f 2 5 is approximately OA 2 5 OB 2 OC 2 5 OD 1 25 OE 2
- Q Consider the position function s t 4 9t 29t 17 Complete the following table with the appropriate average velocities and then make a conjecture about the value of the instantaneous...
- Q Jo 1 4 O A In 1 4 O B jarctan 24 O C j arcsin 22 O D In 1 x4 O E arctan z
- Q 5 6 The graph of a function f is given a At what numbers a does limx a f x not exist b At what numbers a is f not...
- Q A rock is dropped off the edge of a cliff and its distances in feet from the top of the cliff after t seconds is s t 16t Assume the...
- Q The slope of the line normal to the curve ex x 2 10 at the point 0 3 is OA O B 6 O C 6 O D 6 OE...
- Q Consider the position function s t 16t 104t representing the position of an object moving vertically along a line Sketch a graph of s with the secant line passing through...
- Q 3 Write the equation of a vertical line passing through 8 5
- Q 2 Which of the following equations is perpendicular to the graph of 4x 3y 10 A 3x 4y 10 B 4x 3y 10 C 3x 4y 12 1 D 3y...
- Q 3 6 A linear function contains the points 2 5 and 15 20 Does the point 43 53 also lie on the line Explain 2
- Q 4 Line 1 passes through the points 2 5 and 6 k and is perpendicular to the line given by y 1 x 1 5 Find the value of k
- Q The graph of f x is shown below along with the line y x C a y x y f x d Click here for long description O D d...
- Q 1 Write the equation of the line that is perpendicular to y 5x and passes through 7 2
- Q 1 The shaded regions R and R shown below are enclosed by the graphs of f x x and g x 2 R R I A Find the x and...
- Q 2 The region R is a rectangle with vertices P a Ina Q a 0 S 3 0 and T 3 Ina where 1 a 3 201 1 54 05...
- Q X O A B M dx 23 2 C 2 23 2 C C 223 23 2 C O D In 23 23 2 C O E x In 23...
- Q The region in the first quadrant enclosed by the curves y 0 x 2 x 5and is rotated about the x axis The volume of the solid generated is 1...
- Q O A e 3 C Fe O B e C OC 255 22 C O D e 3 C O E Fe C
- Q g x x3 2x 1 What is the slope of the tangent line to the curve g x at the point 2 1 O A 1 OB 5 O C...
- Q The position of an object moving vertically along a line is given by the function s t 4 9t2 26t 17 Find the average velocity of the object over the...
- Q A 25 ft ladder is leaning against a vertical wall At what rate with respect to time is the angle between the ground and the ladder changing if the top...
- Q 3 a From the given graph of f state the numbers at which f is discontinuous and explain why b For each of the numbers stated in part a determine...
- Q O A 2 ln sin 0 2 4 C OB In sin 0 2 4 C O c 2 ln cos 0 2 4 C O D In cos 0...
- Q g x x 2x 1 What is the slope of the tangent line to the curve g x at the point 2 1 O A 1 OB 5 OC 8...
- Q z 2 x y is an equation for the tangent plane to z f x y at the point 0 0 Which of the following is the linear approximation for...
- Q Suppose that f x y is a differentiable function Which of the following are correct statements Select all that apply fx x y lim h 0 O O fy x...
- Q Suppose z 1 2x 3y is an equation for the tangent plane to z f x y at 0 0 Then we also know that select all that apply Of...
- Q 2 Iff is continuous on what can you say about its graph
- Q 25 x Find the points of discontinuity of f For each of them give the number Cat which the discontinuity occurs and the values of both one sided limits Enter...
- Q Consider the graph of the function g given by g x Remember that one Let A x be the area of the shaded rectangle shown in the figure below where...
- Q Hint try the substitution u x O A arcsin x C OB B arcsin u C c arcsin x C O C D x arcsin x C O E 2...
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